Molecular Viewpoints in Nuclear Structure

Abstract

A study of the transition between the $\mathrm{H}_2^{}{}_{}{}^{+}$ molecule and the corresponding three-body nucleus shows (1) that it is useful to regard the system as composed of two parts (heavy particle; heavy and light particles) between which acts an effective potential; (2) that this potential depends more and more on the relative velocity of the two parts as the masses of the light and heavy particles approach equality; (3) that the wave equation and the potential for the relative motion are obtained in a consistent manner by requiring that a certain form of approximate wave function give the best possible representation of the motion of the three particles, in the sense of the variation principle. This wave function represents a state in which the system resonates between the groupings atom-ion and ion-atom. It is adapted to the treatment of the scattering of neutrons in deuterium and is also used in the text to calculate the binding energy of ${\mathrm{H}}^3$. Application of the same type of approximate wave function to the description of nuclear structure in general, gives rise to the concept of resonating group structure. This picture regards the constituent neutrons and protons as divided into various groups (such as alpha-particles) which are continually being broken and reformed in new ways. Group theory gives information as to which groupings are most important in describing a particular state of a given nucleus. The interchange of neutrons and protons between the groups is rapid. It is largely responsible for the intergroup forces, but also prevents one from attributing any well-defined individuality to the groups except as follows: If the time required for a particle to diffuse between two parts of the nucleus vibrating in opposite phase (in the language of the liquid droplet model) is large in comparison with the period of the vibration, then the particles of the nucleus may be divided into groups which preserve their identity long enough to make possible a simple description of the nuclear motion in terms of the relative displacements of these clusters. Arguments are given to show that the diffusion condition is satisfied for low excitation energies. When the nuclear energy is higher, the groups have significance only in providing a suitable mathematical scheme to treat the nuclear motion (see following paper). Allowed types of motion and energies for low states of ${\mathrm{Be}}^8$, ${\mathrm{C}}^{12}$, and ${\mathrm{O}}^{16}$ are calculated in terms of the relative motion of alpha-particle groups, using the methods familiar in molecular structure. The modes of vibration are closely related to those given by the liquid model of Bohr and Kalckar, but many low levels are excluded on symmetry grounds. The general methods outlined here for the description of nuclear structure are to a large extent independent of the nature of the forces between elementary particles. A discussion of the possible existence of many-body forces is given (i.e., forces which cannot be described by a potential that is a sum of potentials involving two particles at a time). The observed variation of nuclear binding energy with atomic number is found not to give sufficient evidence from which to draw any general conclusion. Electron positron theory indicates that a part of the nuclear forces consists of many-body interactions.